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Chen, Lian; Mehboob, Abid; Ahmad, Haseeb; Nazeer, Waqas; Hussain, Muhammad Tahir; Farahani, Mohammad Reza

doi:10.1155/2019/8696982

Cited by 7 publications

(3 citation statements)

References 31 publications

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“…The Hosoya polynomial and related topological indices have been computed for cactus chains, one-pentagonal carbon nanocones and concatenated pentagonal rings [28][29][30]. The distance-based topological indices of nanosheets, nanotubes, and nanotori of SiO 2 with potential applications in food, drug and cosmetic industries have also been calculated [31]. The Hosoya polynomials with other distance based polynomials have been calculated for TOX(n), RTOX(n), TSL(n) and RTSL(n) networks, circumcoronene series of benzenoid H k and carbon pentachains [32][33][34][35].…”

Section: Introductionmentioning

confidence: 99%

On Hosoya Polynomial and Subsequent Indices of C4C8(R) and C4C8(S) Nanosheets

et al. 2022

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Chemical structures are mathematically modeled using chemical graphs. The graph invariants including algebraic polynomials and topological indices are related to the topological structure of molecules. Hosoya polynomial is a distance based algebraic polynomial and is a closed form of several distance based topological indices. This article is devoted to compute the Hosoya polynomial of two different atomic configurations (C4C8(R) and C4C8(S)) of C4C8 Carbon Nanosheets. Carbon nanosheets are the most stable, flexible structure of uniform thickness and admit a vast range of applications. The Hosoya polynomial is used to calculate distance based topological indices including Wiener, hyper Wiener and Tratch–Stankevitch–Zafirov Indices. These indices play their part in determining quantitative structure property relationship (QSPR) and quantitative structure activity relationship (QSAR) of chemical structures. The three dimensional presentation of Hosoya polynomial and related distance based indices leads to the result that though the chemical formula for both the sheets is same, yet they possess different Hosoya Polynomials presenting distinct QSPR and QSAR corresponding to their atomic configuration.

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Section: Introductionmentioning

confidence: 99%

On Hosoya Polynomial and Subsequent Indices of C4C8(R) and C4C8(S) Nanosheets

et al. 2022

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“…Calculating these TIs can be difficult in some cases. Many polynomials have been defined to overcome this issue [7–11]. One of them is the M‐polynomial for the TIs that depend on the degree [12–17].…”

Section: Introductionmentioning

confidence: 99%

Topological indices and QSPR modeling of some novel drugs used in the cancer treatment

Havare

2021

Int J of Quantum Chemistry

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Cancer is a deadly disease. There is no drug yet for the treatment of some types of cancer. New drug trials are being conducted to treat this disease. One of them is HDAC‐based multi‐target drugs. Topological indices (TIs) are the numerical descriptors of a molecular structure obtained by the molecular graph. TIs can be used in the structure–property relationship (QSPR) and structure–activity relationship studies to provide information about the physicochemical properties and biological properties of molecules. In this paper, vorinostat, tucidinostat, triciferol, and CUDC‐101 and CUDC‐907, which are seen as an important light in cancer treatment, are studied. M‐polynomials based on degree and NM‐polynomials based on the sum of degrees of neighboring vertices for chemical graphs of these drugs are calculated. By using these polynomials, many TIs that depend on the degree and the sum of neighboring degrees are obtained. Moreover, The QSPR models are designed using these TIs to estimate some physicochemical properties of these drugs. The QSPR studies are obtained using the curvilinear regression method.

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“…Filipovi et al computed [16]. Chen et al studied the application in chemical graphs in [17]. Yang et al calculated the edge dimension of some families of wheel-related graphs in [18].…”

Section: Introductionmentioning

confidence: 99%

Edge Metric Dimension of Some Classes of Toeplitz Networks

Alrowaili

Zahid

Ahsan

et al. 2021

Journal of Mathematics

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Toeplitz networks are used as interconnection networks due to their smaller diameter, symmetry, simpler routing, high connectivity, and reliability. The edge metric dimension of a network is recently introduced, and its applications can be seen in several areas including robot navigation, intelligent systems, network designing, and image processing. For a vertex s and an edge g = s 1 s 2 of a connected graph G , the minimum number from distances of s with s 1 and s 2 is called the distance between s and g . If for every two distinct edges s 1 , s 2 ∈ E G , there always exists w 1 ɛ W E ⊆ V G , such that d s 1 , w 1 ≠ d s 2 , w 1 ; then, W E is named as an edge metric generator. The minimum number of vertices in W E is known as the edge metric dimension of G . In this study, we consider four families of Toeplitz networks T n 1,2 , T n 1,3 , T n 1,4 , and T n 1,2,3 and studied their edge metric dimension. We prove that for all n ≥ 4 , e dim T n 1,2 = 4 , for n ≥ 5 , e dim T n 1,3 = 3 , and for n ≥ 6 , e dim T n 1,4 = 3 . We further prove that for all n ≥ 5 , e dim T n 1,2,3 ≤ 6 , and hence, it is bounded.

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Hosoya and Harary Polynomials ofTOX(n),RTOX(n),TSL
Lian Chen
¹
,
Abid Mehboob
²
,
Haseeb Ahmad
³

et al.

Cited by 7 publications

References 31 publications

On Hosoya Polynomial and Subsequent Indices of C4C8(R) and C4C8(S) Nanosheets

On Hosoya Polynomial and Subsequent Indices of C4C8(R) and C4C8(S) Nanosheets

Topological indices and QSPR modeling of some novel drugs used in the cancer treatment

Edge Metric Dimension of Some Classes of Toeplitz Networks

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Hosoya and Harary Polynomials ofTOX(n),RTOX(n),TSLLian Chen1, Abid Mehboob2, Haseeb Ahmad3 et al.

Cited by 7 publications

References 31 publications

On Hosoya Polynomial and Subsequent Indices of C4C8(R) and C4C8(S) Nanosheets

On Hosoya Polynomial and Subsequent Indices of C4C8(R) and C4C8(S) Nanosheets

Topological indices and QSPR modeling of some novel drugs used in the cancer treatment

Edge Metric Dimension of Some Classes of Toeplitz Networks

Contact Info

Product

Resources

About

Hosoya and Harary Polynomials ofTOX(n),RTOX(n),TSL
Lian Chen
¹
,
Abid Mehboob
²
,
Haseeb Ahmad
³

et al.